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Advances in Mathematical Physics
Volume 2017, Article ID 6754780, 7 pages
https://doi.org/10.1155/2017/6754780
Research Article

Remarks on Pressure Blow-Up Criterion of the 3D Zero-Diffusion Boussinesq Equations in Margin Besov Spaces

Min Fu1,2 and Chao Cai1

1State Key Laboratory for Multispectral Information Processing Technologies, School of Automation, Huazhong University of Science and Technology, Wuhan, China
2College of Science, Wuhan Institute of Technology, Wuhan, China

Correspondence should be addressed to Chao Cai; nc.ude.tsuh@oahciac

Received 13 February 2017; Accepted 6 March 2017; Published 24 April 2017

Academic Editor: Pavel Kurasov

Copyright © 2017 Min Fu and Chao Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study is focused on the pressure blow-up criterion for a smooth solution of three-dimensional zero-diffusion Boussinesq equations. With the aid of Littlewood-Paley decomposition together with the energy methods, it is proved that if the pressure satisfies the following condition on margin Besov spaces, for then the smooth solution can be continually extended to the interval for some . The findings extend largely the previous results.